Electrically Small Microstrip Antennas Targeting Miniaturized

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Electrically Small Microstrip Antennas TargetingMiniaturized Satellites: the CubeSat Paradigm

Constantine Kakoyiannis and Philip ConstantinouMobile Radio Communications Laboratory

School of Electrical and Computer EngineeringNational Technical University of Athens

Greece

1. Introduction to the CubeSat space programme

A CubeSat is a type of miniaturized satellite used primarily by universities for space explorationand research, typically in low Earth orbits (e.g. sun-synchronous). The design protocolspecifies maximum outer dimensions equal to 10 × 10 × 10 cm3, i.e., a CubeSat occupiesa volume up to 1 litre (CubeSat programme, 2010). CubeSats weigh no more than1.0 kg, whereas their electronic equipment is made of Commercial Off-The-Shelf (COTS)components. Several companies have built CubeSats, including large-satellite maker Boeing.However, the majority of development comes from academia, with a mixed record ofsuccessfully orbited Cubesats and failed missions (Wikipedia, 2010a).Miniaturized satellites, or small satellites, are artificial orbiters of unusually low weights andsmall sizes, usually under 500 kg. While all such satellites can be referred to as small satellites,different classifications are used to categorize them based on mass (Gao et al., 2009):

1. Mini-satellite (100–500 kg)

2. Micro-satellite (10–100 kg)

3. Nano-satellite (1–10 kg)

4. Pico-satellite (0.1–1 kg)

5. Femto-satellite (0.01–0.1 kg)

CubeSats belong to the genre of pico-satellites; their maximum weight lies on the borderlinebetween pico- and nano-satellites. The main reason for miniaturizing satellites is to reducethe cost of deployment: heavier satellites require larger rockets of greater cost to finance;smaller and lighter satellites require smaller and cheaper launch vehicles, and are oftensuitable for launch in multiples. They can also be launched “piggyback”, using theexcess capacity of larger launch vehicles (Wikipedia, 2010b). But small satellites are notshort of technical challenges; they usually require innovative propulsion, attitude control,communication and computation systems. For instance, micro-/nano-satellites have to useelectric propulsion, compressed gas, vaporizable liquids, such as butane or carbon dioxide,or other innovative propulsion systems that are simple, cheap and scalable. Micro-satellitescan use radio-communication systems in the VHF, UHF, L-, S-, C- and X-band. On-boardcommunication systems must be much smaller, and thus more up-to-date than what is used

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in conventional satellites, due to space constraints. Furthermore, miniature satellites usuallylack the power supply and size required for conventional bulky radio transponders. Variouscompact innovative communication solutions have been proposed for small satellites, suchas optical (laser) transceivers, antenna arrays and satellite-to-satellite data relay. Electronicsneed to be rigorously tested and modified to be “space hardened”, that is, resistant to theouter space environment (vacuum, microgravity, thermal extremes and radiation exposure)(Wikipedia, 2010b).The CubeSat programme was developed through the joint efforts of research laboratories fromCalifornia Polytechnic State University (Cal Poly) and Stanford University, beginning in 1999.The concept was introduced to the scientific community as an opportunity for all universitiesto enter the field of space science and exploration. A large group of universities, along withcertain companies and organizations, participate actively in the CubeSat programme; it isestimated that 40 to 50 universities were developing CubeSats in 2004. Featuring both smallsize and weight, a CubeSat can be built and launched for an estimated total of $65,000–80,000(per fiscal year 2004 values). The standard 10 × 10 × 10 cm3 basic CubeSat is often called a“1U” CubeSat, meaning one unit. CubeSats are roughly scalable in 1U increments and larger.The four basic sizes are 0.5U, 1U, 2U and 3U. The number corresponds to the length of theCubeSat in decimetres; width and depth are always 10 cm, or 1 dm. Orbiters such as a “2U”CubeSat (20 × 10 × 10 cm3) and a “3U” CubeSat (30 × 10 × 10 cm3) have been both built andlaunched. Since CubeSats are all 10 × 10 cm2 (regardless of length) they can all be launchedand deployed using a common deployment system. CubeSats are typically launched anddeployed from a mechanism called a Poly-PicoSatellite Orbital Deployer (P-POD), developedand built by Cal Poly. The low cost of the CubeSat programme, compared to standard satellitemissions, has formed a cost-effective independent means of getting a payload into orbit formany institutions around the world. Most CubeSats carry one or two scientific (measuring)instruments as their primary mission payload (Wikipedia, 2010a). Only few of them areequipped with a propulsion system that enables orbit correction or attitude control. One suchexample is the CubeSat built by the University of Illinois, which was loaded with an array ofsmall ion thrusters.CubeSats enable a vast array of research possibilities and applications. One of the key areas ofstudy is Earth remote sensing: efforts there focus on earthquake detection through the detectionof magnetic signals, study of the air-glow phenomenon in the Earth’s atmosphere, cosmicdust detection and the possibility of terrestrial gamma-ray bursts originating from lightning.Another field of study, and a rather expensive one, is biology. For instance, the GeneSat-1project by NASA was not cheap by CubeSat standards: total expenditure on the satellite andits experiments reached $6 million before GeneSat was launched on a Minotaur rocket. Itsmission is to establish methods for studying the genetic changes in bacteria exposed to a spaceenvironment (Wikipedia, 2010a). Modern small satellites are also useful for other applications,such as telecommunications, space science, mitigation and management of disasters (floods,fire, earthquake, etc.), in-orbit technology verification, military applications, education, andtraining (Gao et al., 2008; 2009).CubeSat missions started in 2003; that year 5 academic and 1 commercial CubeSat werecarried into orbit. Successful launches continued in 2005 with 3 more CubeSats built byuniversities; 17 more satellites were carried into orbit between 2007 and 2010. But, in 2006,July saw the greatest disaster in the short history of CubeSats: with a payload of 14 satellitesfrom 11 universities and a private company, a DNEPR-1 rocket was launched from BaikonurCosmodrome, Kazakhstan; it was the largest planned deployment of CubeSats to date. The

274 Microstrip Antennas

rocket failed and crashed into the ground, obliterating the CubeSats and 4 other satellitesaboard. The launch was lost after the engine responsible for the first stage of lift off stoppedworking prematurely. Thrust termination occurred at 74 seconds after lift off (Wikipedia,2010a). An extensive (but incomplete) list of CubeSat missions can be found in (Wikipedia,2010c). Out of the 52 past missions documented, 24 are currently active; 1 was successful buthas been de-activated; 23 satellites failed; and the status of 4 others is unclear. Out of the 23missions that failed, 17 cases were launch failures; the other 6 were successfully carried intoorbit, but a malfunctioning system prevented them from becoming operational.Since 2001, there has been a growing number of European universities that build andcontribute their own pico-satellite(s) to the programme. The efforts of research groups fromuniversities in Denmark, Germany and the UK have been particularly instrumental to thedevelopment of CubeSat technology.

2. Scope of the chapter

Modern small satellites require antennas to realize the following four fundamental functions,and CubeSats are no exception to the norm:

1. Telemetry, tracking and command (TTC),1 which includes both uplink and downlink, atdifferent frequencies

2. High-speed downlink for payload data, e.g., in Earth-observation missions

3. GPS/GNSS signal reception

4. Inter-satellite cross links

These functions often require several different antennas. Basic radiator configurations usedare normally helices, monopoles, patches, and patch-excited cups, depending on frequencyrange, coverage requirements, and application (Gao et al., 2008; 2009).Before moving on to the objectives of the Chapter, a few comments on frequency allocationsare in order. Since CubeSats are mostly developed in academic research centres, it is easy todeduce that they are almost solely intended for educational and research (i.e., non-commercial)purposes. Therefore, there is a frequency allocation problem, because CubeSats could notoccupy commercial spectrum. In Europe, certain frequency bands have been allocated foramateur satellite communication purposes. Examples of these frequencies are the 434.8–438,1260–1270 and 2400–2450 MHz bands. In the US, although not strictly termed “amateursatellite”, nine frequency bands have been allocated for space research. These bands fall inthe 400–2700 MHz range. The most commonly used ones are 2025–2110 and 2200–2290 MHz.This Chapter addresses the problem of building nano-/pico-satellites from the antennadesigner’s point-of-view. Our objective is to describe the implementation of a planar,low-cost antenna solution for the TTC subsystem of a 1U CubeSat orbiter, operating in the434.8–438 MHz band; this band, also known as the “70-cm” band, is often chosen by systemdesigners due to favourable path loss characteristics. A radiator backed by a ground planeis required, so as to obtain “single-sided” directivity. These three initial specifications can bemet with proper design of microstrip “patch” antennas. Patch antennas are manufacturedusing standard Printed Circuit Board (PCB) techniques; space-graded substrate materialsmust be used to satisfy the tighter mechanical and thermal constraints of space applications.A planar antenna is essentially a two-layer PCB, and thus it costs much less than a standard4-layer or 6-layer PCB. What is more, if the designer implements a feeding network without

1 Often abbreviated also as “TT&C”.

275Electrically Small Microstrip Antennas Targeting Miniaturized Satellites: the CubeSat Paradigm

any metallized holes (Vias), manufacturing costs drop even further. Nonetheless, it is arather challenging design task to integrate a planar radiator that resonates at a wavelengthλ0 = 687.3 mm on a 100 × 100 mm2 surface. Herein, λ0 denotes the free-space wavelength.The implementation of the CubeSat antenna is based on the following key assumptions. Thesatellite is built on a cubic conductive chassis having 10-cm sides. One of the six faces istotally used up by the antenna. Thus, the surface on which the antenna will be printed is a100-mm square that will be occupied by the substrate in its full extent. The patch antennamust have both sides shorter than 100 mm. Moreover, it has been also assumed that thefeed network of the antenna will reside either on a different face of the cube, or on theinside with the rest of the electronics, but definitely not on the same face as the antenna.In the latter case, antenna excitation is done with a protruding coaxial probe, i.e., a coaxialtransmission line whose center conductor runs through the substrate. Last but not least,since this application is oriented towards satellite communications, it has been assumed thatthe microstrip antenna should have the ability to produce circularly polarized waves. Arobust technique for the generation of circular polarization from patch antennas is the dualfeed with signals in phase-quadrature. For this scheme to work, the shape of the microstrippatch, which determines the shape of the Surface Current Distribution (SCD), must displaytwo perpendicular symmetry axes; otherwise, polarization will come out elliptical at best.At the centre frequency f0 = 436.5 MHz we get a free-space wavelength λ0= 687.3 mm.The size of a patch antenna should be at least equal to λg

2 × λg2 , where λg is the guided

wavelength inside the cavity formed by the substrate and the two copper layers (Top andBottom). If we had used a low-permittivity substrate with εr ≈ 1.0 (e.g. Arlon FoamClad™),which is desirable for microstrip antennas, then the dimensions of the patch would beλ02 × λ0

2 = 343.6 × 343.6 mm2. In that case, the antenna would require 12 times the areathat is available on the satellite.From the above introductory design notes it becomes obvious that the designer is forced touse extensive Dielectric Loading (DL) to obtain an initial degree of miniaturization. As it willbe demonstrated in the following sections, DL alone is not sufficient in order to achieve therequired total miniaturization. In any case, the high–εr material is bound to have a detrimentaleffect on bandwidth. To lessen this side-effect, a thick substrate has been chosen. To avoidfurther degradation of the radiation efficiency, the material should display low loss tangent(tan δe). The above issues preclude the use of a low-cost material, such as FR-4; the choices leftto the designer are high-quality space-graded materials, such as PTFE, ceramic and alumina.This Chapter is intended for serving the antenna engineering community as a concise designguide to a specific class of microstrip antennas, particularly inductive-slit-loaded microstripantennas. However, the design approach and the electromagnetic modelling are applicableto any sort of microstrip antenna. This design guide will be useful for senior undergraduateand graduate students, research engineers, and practising antenna engineers in the field ofprinted/planar antennas. A basic understanding of electromagnetic theory and antennas isrequired.The Chapter is organized as follows. Section 3 attempts an exhaustive review of existingliterature on small-satellite-oriented antennas. Section 4 documents the design of the hybridcoupler which feeds the antenna with two equal-amplitude signals in phase-quadrature. Thesimulation environment is also described, along with details of the simulation setup usedthroughout the Chapter. Section 5 describes in detail the design procedure of the antennaand the miniaturization techniques employed. A large array of numerical results is given forthis two-step design procedure. Section 6 discusses the simulation results and examines the


electrical performance of the antenna in terms of its electrical size. Finally, Section 7 concludesthe Chapter with a summary of key findings and suggestions for further research.

3. Antennas for modern small satellites: Literature survey

The development of the antenna described herein can commence directly from systemspecifications. However, good engineering practice dictates that the relevant literature besurveyed first. After the state-of-the-art of the field has been determined, the antenna engineercan make a more educated guess on the course of action. Non-planar designs used arenormally helices, monopoles, and open waveguides. Planar structures are usually patchesand patch-excited cups. The choice depends on frequency range, coverage requirements, andapplication.This Section aims to serve as an introduction to what is undoubtedly a fascinating andimportant part of the future of satellite antennas.

3.1 Wire Antennas and other non-planar structuresThe literature review first revealed a number of studies oriented towards small satellitesoperating in the 70-cm band that are equipped with linear monopole or dipole antennas builtwith measuring tape. The tape remains folded while the satellite is not yet in orbit, and is heldin place with Nylon fibres, which are secured using a short length of Nichrome wire insidethe satellite. Once the satellite is in orbit, current passes through the Nichrome wire, the fibresmelt and the linear antenna is released. Small satellites using this linear-antenna techniqueare studied in (Dabrowski, 2005; Galysh et al., 2000; Heidt et al., 2000; Hunyadi et al., 2002;LaBerteaux et al., 2007; Mizuno et al., 2005; Puig-Suari et al., 2001; Schaffner & Puig-Suari,2002).But this is not the only available option in terms of wire antenna elements. (Moghaddam etal., 2004) used a separated turnstile antenna (STA) to obtain saddle-shaped and hemisphericalpatterns for small low-earth-orbit (LEO) satellites at VHF and UHF bands. This STA is an arrayof four monopoles that are mounted symmetrically on the satellite and are electrically drivenin phase-quadrature. The antenna is built with 55 cm–long wire elements and it resonates at130 MHz. Dual-band operation in the UHF band is possible by exploiting the next naturalodd (third-harmonic) resonance of the monopoles at 390 MHz. Gain in the UHF band wasspecified at 5 dBi.Helices, despite being protruding radiators like monopoles, are also popular solutions.Quadrifilar helical antennas (QHAs) are suitable for small LEO satellites not only for theirgain pattern, but also due to their low weight, size and cost. The QHA is made up of fourcoaxial identical elements, which are fed in phase-quadrature to produce circular polarization.(Rezaei, 2004) designed an S-band QHA for the TTC subsystem of the Small Multi-MissionSatellite that covers the Asia-Pacific region. The antenna operates at 2.26 GHz providinga 2% fractional bandwidth at VSWR = 1.3 : 1. If we denote the VSWR level by S, thenfractional bandwidth scales by the factor (S − 1)/(2

√S) (Yaghjian & Best, 2005). Thus, at a

level VSWR = 2 : 1 the bandwidth is estimated at 5.4%. Based on the author’s description,the electrical size of this radiator, omitting the ground plane, was estimated at ka = 2.11 rad.2

The result was anticipated, since QHAs are invariably electrically large antennas.The G-shaped wire monopoles designed by (Yousuf et al., 2008) specifically target CubeSatmissions. This rhombic structure is based on the concept of the loaded monopole, where a

2 See Section 5.6 and Fig. 32 for the definition and importance of electrical size.


short monopole is loaded with two rectangular rings. Three versions were designed; two forthe VHF (150 and 180 MHz) and one for the UHF band (370 MHz). Initial designs were doneon infinite ground planes. Mounted this way, the achieved numerical bandwidths rangedbetween 32–42%. Bandwidth definition is ambiguous, since the authors used multiple systemimpedances. In any case, once the G-shaped monopoles where mounted on a finite wire-gridmodel of a CubeSat, their numerical electrical performance was severely affected, particularlythat of the VHF versions. This is also to be expected: monopole antennas work fine as longas their ground plane is large enough. Below a certain limit, chassis-coupling-and-excitationconsiderations must be included in the design cycle. The electrical size of the VHF antennaswas (ka)VHF = 1.26 rad, whereas that of the UHF antenna was (ka)UHF = 1.41 rad, i.e.,slightly smaller than the size of the half-wavelength dipole. The ground plane was ignored inthese estimations.The size of helices can be reduced either by modifying the helical structure or by introducingdielectric loading (DL). Little design freedom is obtained by varying the pitch angle anddiameter of the helix to reduce its size without destroying its performance. Moreover,the ground plane of helical antennas needs to remain large enough for good performance.However, DL strengthens the near field, increases the quality factor, and reduces theoperational bandwidth of the helix. (Niow et al., 2009) proposed a well-balanced combinationof a modified helical antenna and DL to reduce antenna size. The modified structurewas a backfire bifilar helical antenna (BBHA), which, unlike conventional helices, does notrequire a ground plane. This structure is still relatively large, thus a dielectric rod wasintroduced around the feeding coaxial cable to reduce the size further. The dielectric rodwas bound to affect antenna gain and bandwidth. Therefore, trade-offs were made betweensize reduction and antenna performance. All developed antennas operated at 2.6 GHz. Thechosen performance metrics were broadband gain and axial ratio (AR) bandwidth. The initial(unloaded) BBHA featured a gain of 4 dBi and an AR bandwidth equal to 0.8 GHz. Itselectrical size is calculated at (ka)ini = 2.22 rad. The second BBHA was loaded with a Teflonrod. It featured a peak gain of 4 dBi and an AR bandwidth equal to 0.4 GHz. Its electrical sizewas reduced by 19.5% to a new value of (ka)Teflon = 1.78 rad. The third BBHA was loadedwith a Macor rod. It featured a peak gain of 3.7 dBi and an AR bandwidth equal to 0.4 GHz.Its electrical size was reduced by 24% to a new value of (ka)Macor = 1.72 rad. Note that theelectrical size of a half-wavelength dipole equals (ka)λ/2 = 1.57 rad.High-frequency bands, like the X-band, provide for physically small antennas regardlessof structure. (Galván & Colantonio, 2009) implemented a waveguide-based antenna forthe data-downlink subsystem of the SAC-D/AQUARIUS mission, which is a LEO earthobservation satellite. The radiating part is a compact choke ring antenna with reducedback-radiation. The structure consists of a segment of circular waveguide surrounded byequally spaced concentric rings (“corrugations”). Flaring of the waveguide was not allowed,in order to avoid narrowing the beam; a hemi-spherical pattern was thus obtained, accordingto specifications. The antenna operates at 8.2 GHz with a 5% fractional bandwidth and a gainof 7.4 dBi. The electrical size of the radiating element alone was calculated at ka = 2.99 rad.This part of the literature survey is concluded with the recent study by (Nohmi et al., 2010), inwhich the authors implemented a solar paddle antenna for the “KUKAI” pico-satellite missionof the Kagawa University, Takamatsu, Japan. The solar paddle antenna is a bent wire radiatorinstalled around the circumference of the solar paddle. This is a low-cost implementation,since it requires only a segment of wire and a few ferrite beads to separate the power supplyline from high-frequency signals. This type of antenna simplifies the structure of the satellite,


reduces its weight and provides the necessary directivity. From the manuscript it is notparticularly clear whether a single antenna or two antennas have been integrated into theperiphery of the solar paddle. The radiating system operates at the VHF (145 MHz) and theUHF band (435 MHz); these two frequencies are harmonically related. Furthermore, it isclear that at the lower frequency the radiator is a λ/4–long monopole, whereas at the upperfrequency the radiator is a 3λ/4–long monopole.

3.2 Planar antennas for modern small satellitesOne of the earliest studies on planar antennas for small satellites appeared in (Tanaka et al.,1994). To preserve area for both antenna and solar cells on a micro-satellite, the authorsdesigned the radiating system with the solar panels attached on top of the patch antenna.The concept behind this stacked configuration is that a patch antenna, being a lossy cavity,radiates through the fringing fields appearing at its open-circuited edges. Therefore, it isirrelevant whether the solar panel is transparent to radio waves or not; the solar panel needsonly to be placed in such a manner that its own power generation function as well as theradiation performance of the patch beneath it are both maintained. To this end, solar cellscan occupy the whole surface of the patch and of the surrounding substrate, except for theregion where the radiating fringing fields appear, that is, the area immediately surroundingthe patch. The prototype antenna operated at 2.225 GHz with a 1.5% fractional bandwidth.Microstrip antennas have three main feed methods: transmission line feed, optionally inset;coaxial probe feed; and aperture coupling. In (He & Arichandran, 2001), where the focusis again on micro-satellites, the authors designed a physically small, aperture-coupled patchantenna at 10.74 GHz (X-band). The antenna displays a 5.6% fractional bandwidth and a gainof 6.5 dBi (both numerical). Radiation efficiency was estimated at nrad = 0.85 = −0.7 dB. Theelectrical size of the radiating element was calculated at ka = 1.28 rad.In (Mathur et al., 2001) the authors describe the design of two patch antennas for the USUsatnano-satellite which is part of the ION–F constellation. The uplink antenna works at 450 MHz,and it is printed on a substrate with εr = 10.2. It also achieves a bandwidth of 7 MHzat VSWR = 2 : 1 (1.6%), whereas the square patch has a side length equal to 106.7 mm.To achieve circular polarization with a single feed, a coaxial probe feeds the patch alongits diagonal. Its electrical size was calculated from the authors’ description to be equal to(ka)UHF = 0.71 rad. The downlink antenna resonates at 2.26 GHz and displays 4.9 dBi gainand a 17 MHz bandwidth (0.8%). It was designed on the same substrate, and it is a 20-mmsquare patch, thus it is estimated that (ka)S−band = 0.67 rad. Size estimations are somewhatoptimistic, since they take into account only the size of the patch, leaving out the spread of thecurrent distribution on the ground plane.The next study, which deals specifically with a CubeSat planar antenna, was conducted by(Fujishige et al., 2002) and (Tamamoto & Shiroma, 2002) in the framework of the CubeSatprogramme of the University of Hawaii. It addresses the design of a type of active antennabetter known as a “grid oscillator”, which is essentially a C-band active antenna array. Anarray of active semiconductor devices (transistors) are embedded in a grid of copper tracesprinted on a substrate, which serves as a DC bias distribution circuit, RF-embedding circuitand radiator. The authors in (Fujishige et al., 2002) used pHEMT devices and built a 6 × 6transistor matrix on a Rogers Duroid™ substrate (εr = 10.2) at 5.85 GHz. The structure isbacked by the conductive chassis of the CubeSat, which serves as a mirror to provide thenecessary excess feedback for oscillation. The horizontal traces of the matrix function as DCbias lines. The vertical traces are the radiating elements, producing a vertically polarized


array that does not interact with the bias lines. The grid oscillator is actually the microwaveequivalent of a laser:

1. A lossy cavity is formed by the structure and the mirror.

2. As soon as DC power is applied, oscillation is triggered by transients and/or noise; eachtransistor oscillates at a different frequency.

3. A non-coherent wave originates from the grid, bounces off the mirror and injection-locksthe active devices; the cavity starts to reverberate.

4. Different eigenmodes compete inside the cavity, just as in a laser. Higher-order modeslose most of their power to diffraction. Single-frequency, self-locked, coherent oscillationis what remains from this process.

5. The output power from each device is combined in the far-field, making thispower-combining scheme very efficient.

Unlike regular phased arrays, the spacing between the vertical traces is on the order ofλ0/10, making the grid oscillator very compact at microwave frequencies. Indeed, the outerdimensions of the grid oscillator in (Fujishige et al., 2002) were a mere 50 × 70 mm2.Several planar antennas were built to address the communication needs of European smallsatellite missions, such as the ESEO and SSETI-Express student missions. The size of themini-satellite described in (Wincza et al., 2004) is 60 × 60 × 60 cm3 and it communicates at2.025 GHz and 8.45 GHz. However, very little information is given on the topology and theelectrical performance of the antenna, except an operational bandwidth of 50 MHz. Besides,the design procedure is unclear, since the microstrip patch is printed on a complex sandwichedstructure to increase the bandwidth. The ESEO satellite, studied in (Idzkowski et al., 2004),communicates at 2.080 GHz and 2.260 GHz, and bears a total of six microstrip antennas forcommunications and telemetry. The authors cite a 7-dBi gain for this antenna system, withoutclarifying whether this gain holds for each antenna separately or if the antennas were groupedin two 3-element linear arrays. Their study focuses mainly on the details of the link budget ofthe ESEO mission.(Muchalski et al., 2004) studied low-gain TTC antennas for the ESEO and SSETI-Expressmissions. The main objective of their research was the optimization of antenna placement.The authors designed a 61.4 mm square patch that was suspended 10 mm above the groundplane (air dielectric). The ground plane measured 60 cm × 70 cm and corresponded to the wallsize of the spacecraft. Input impedances and radiation patterns were numerically calculatedfor five different simulation scenarios, which included centre-mounted, edge-mounted andcorner-mounted antennas. The model corresponding to each scenario included a singleantenna. The results confirmed that both Zin(jω) and the radiation pattern were severelyaffected by antenna placement. The centre-mounted antenna was initially designed, andit operated at 2.45 GHz. It featured a 8.2% fractional bandwidth and an electrical size(ka)centre = 2.24 rad. When this patch was moved to either of the edges of the ground plane,the centre frequency shifted to 2.35 GHz. The operational bandwidth changed to 8.5% andthe new electrical size was (ka)edge = 2.15 rad. Finally, when the patch was moved to one ofthe corners of the ground plane, the centre frequency shifted to 2.275 GHz. The operationalbandwidth changed to 7.9% and the new electrical size was (ka)corner = 2.08 rad.The antenna system of the ESEO orbiter has drawn considerable attention. An innovative,light weight, high gain antenna for the high-speed downlink of payload data of the ESEOwas described by (Arnieri et al., 2004). The design is based on the shorted annular patch(SAP), which was integrated with a stacked parasitic element. The mechanical attributes


of SAPs provide for an all-metal antenna (very desirable for space applications) realized insuspended technology, leading to a compact and robust radiator. The stacked configurationprovides the necessary design freedom to adjust gain and beam aperture simply by changingthe distance between the two radiating elements. The nominal half-wavelength distanceturns the structure essentially into a two-element end-fire linear array. The authors excitedtheir antenna through an aperture-coupled feed, which provided circular polarization. Theantenna operated at 2.425 GHz with an 8% fractional bandwidth. Peak measured gain was12.2 dBi. The specified dimensions of the radiating parts lead to an estimated electrical sizeka = 2.50 rad. This structure was later refined in (Arnieri et al., 2007). The updated dimensionsproduce a value ka = 2.73 rad. The stacked SAP antenna is also described in (Gao et al., 2009).Most antenna implementations target either the TTC or the payload data downlinksubsystem. One of the very few studies on inter-satellite cross-link antennas picks up atopic of tremendous interest to array designers: modified Van Atta retrodirective arrayswere proposed for pico-satellites operating at 10.5 GHz (Mizuno et al., 2005). The firstobvious choice for cross-linking satellites is to use omnidirectional antennas. However,this choice is energy-inefficient, wasting valuable satellite resources, while at the same timeit creates a satellite network that is vulnerable to eavesdropping. The second obviousalternative is to design dynamically steerable antenna arrays (“smart beamformers”). Suchan implementation would tax a significant amount of resources in terms of processing power,and would introduce a complexity level that would cancel out the simple, low-cost nature ofsmall satellites. For pico-satellite applications, a suitable alternative to dynamic beam steeringis a self-steering retrodirective array (Mizuno et al., 2005). Retrodirective antennas are able tosense the direction of an incoming radio signal and send a reply back in the same direction. Afascinating property of retrodirective arrays is that this ability results purely from analog/RFsignal processing; no digital signal processing algorithms are required at the digital basebandpart of the transceiver. The topic of modified Van Atta arrays is also discussed in (Gao et al.,2009).The S-band is also used for communication by the commercial SSTL micro-satellite built bySurrey Satellite Technology Ltd. Out of the three antennas described in (Hadj Abderrahmaneet al., 2006), one is a circular patch citing a 4.9-dBi gain and main lobe beamwidth equal to80°; this one is used for command uplink. Apart from a gain variation of 3 dB, no other detailsare given. Moreover, the provided radiation pattern (see Fig. 8 in (Hadj Abderrahmane etal., 2006)) corresponds to 400 MHz, not 2 GHz. Finally, the antenna depicted in Fig. 9 of(Hadj Abderrahmane et al., 2006) does not agree with the cited main-lobe beamwidth, sincethe circular patch seems to be equally wide with its ground plane.(Maleszka et al., 2007) describe briefly the design of a low-profile, low-gain planar antennafor a SSETI-Express mini-satellite; the size of the satellite is 60 × 60 × 70 cm3. The antennais mounted on a 350 × 350 mm2 ground plane and operates at 2.4 GHz. Particular emphasisis placed on circular polarization generation and on maintaining an acceptable axial ratio, sothat controlled degeneration to elliptical polarization is achieved.During the initial acquisition period following the separation of the satellite from the launchvehicle, satellite stabilization has not been achieved yet; thus an omnidirectional antenna isrequired for communication between space and ground segment (the first established TTClink). Various low-gain antennas have been developed for TTC of small satellites at VHF,UHF and the S-band. These antennas are simple, cheap, easily fabricated, and have nearlyomnidirectional or broad-beam radiation patterns, thus the satellite does not need accuratecontrol of its attitude. One such antenna is the microstrip patch described in (Gao et al.,


2008). It uses a circular patch fed by a coaxial probe at the bottom. It is circularly polarizedand operates within a tunable frequency range of 2.0–2.5 GHz, that is, inside an aggregatefractional bandwidth equal to 22%. This patch achieves a gain of 6.5 dBi at an electrical sizeequal to ka = 1.99 rad at 2.25 GHz.Design ideas for small satellite antennas can be borrowed just as well from other segments ofthe antenna field, as long as the structure undergoes the necessary “space” modifications. Inthis context, the compact, dual-band, circularly polarized microstrip antenna (CPMA) by (Lee& Woo, 2008) is reported here. This CPMA was designed for satellite communication handsetsby combining a folded patch and a plate into a stacked 3-D structure. However, the designwas carried out on an electrically large ground plane, thus chassis-coupling-and-excitationconsiderations were not included in the design iterations. The lower band, which correspondsto the downlink, is centred around 1.61 GHz. The CPMA achieves a fractional bandwidthequal to 4.8% and a gain of 2.4 dBi. The electrical size was calculated at (ka)lower = 0.90 rad(the ground plane was ignored in this estimation). The upper band, which corresponds to theuplink, is centred around 2.4865 GHz. The CPMA achieves a fractional bandwidth equal to6.6% and a gain of 5.3 dBi. The electrical size was calculated at (ka)upper = 1.39 rad.The next study deals specifically with planar antennas targetting a CubeSat programme.(Hamrouni et al., 2009) designed and prototyped two microstrip antennas on a 1.6 mm–tallsubstrate. The antennas were intended for use on the first Tunisian pico-satelite ERPSat-1and operated at 2.4 GHz (S-band). Very few details were given on the design strategy.The first prototype achieved a 2.9% fractional bandwidth with an electrical size equal to(ka)1 = 1.62 rad. The second prototype achieved a 3.6% fractional bandwidth and, eventhough dimensions differed, its electrical size was again (ka)2 = 1.62 rad.The little space available on small satellites brings about limited capabilities for the analog/RFsection. (Marrocco et al., 2010) suggested that these limitations can be overcome by exploitingthe idea of “structural radiators”, which has already been implemented in avionics, navalcommunications and hand-held terminals. This concept diverges from the use of independentsets of self-consistent radiators, and instead relies on deliberate exploitation of antenna-chassiscoupling. Accordingly, radio functions are no longer fulfilled by stand-alone antennas (whips,patches, helices, etc.), while, at the same time, the satellite structure is exploited as part of theradiation mechanism. Thus, the problem of antenna integration onto small satellites can beaddressed through a distributed approach, where multiple “exciter” antennas are placed allover the structure and stimulate it to produce a controllable radiation pattern. Strong couplingis expected among the exciters of the satellite, hence they must be treated as a multi-portnetwork, i.e., designed as a whole. In their effort to demonstrate that such a system can beoptimized to produce variable patterns and polarizations, the authors initially developed atunable vertical inverted–F antenna mounted on a finite horizontal ground plane. The antennaoperated at 2.3 GHz and achieved a 5.7% instantaneous fractional bandwidth. When multiplesuch exciters were used to design an eight-element circular array on a finite satellite body, theactive reflection coefficients revealed that bandwidth was increased to 13.9% because of theconfiguration and coupling between the elements.In a very recent study, (Maqsood et al., 2010) presented dual-band, circularly polarized,planar antennas for GNSS-based remote sensing applications. The authors developed a zenithand a nadir antenna that can be body mounted on-board a small UK-DMC satellite. Bothantennas cover both L1 and L2 bands, centred at 1.575 GHz and 1.227 GHz respectively.In terms of compact antenna design, attention is drawn to the zenith antenna, which wasinitially designed as a slot-coupled stacked patch radiator. Three layers were stacked together,


with the square patch antenna on top of the upper two layers. The initial feed networkcomprised of three Wilkinson power dividers, which fed the bottom patch through aperturecoupling. The upper patch was electromagnetically coupled to the lower patch. However,since the numerical results revealed that the radiation pattern had a strong back-lobe, thefeed network was changed. Instead of aperture coupling with the bottom patch, the toppatch was eventually directly connected to the feed network using vias; the bottom patchwas electromagnetically coupled to the upper patch. Wilkinson dividers were replaced bya broadband three-branch coupler. The measured prototype showed a 6.3 dBi gain at theL1 and a 4.0 dBi gain at the L2 band. Calculated electrical sizes based on author data are(ka)L1 = 1.82 rad and (ka)L2 = 1.42 rad, respectively.The literature survey is concluded with three recent review papers of great educationalvalue, particularly for young engineers in the field (Gao et al., 2009; Wettergren et al.,2009; Zackrisson, 2007). A distinct feature of these papers is that, through an abundanceof photographs depicting commercial antennas and arrays, they present state-of-the-artantennas for modern small satellites from the perspective of the industry. Industrial perspectiveis often very different from that of academia, so it could be the “rude awakening” that revealstypes of antennas that have proven viable over time.

3.2.1 Antenna development at Saab SpaceThe first two contributions were made by Saab Space, now RUAG Aeropace Sweden. In(Wettergren et al., 2009; Zackrisson, 2007), the authors present wide coverage antennas forsmall satellites. Depending on frequency range, coverage requirements and application, theproposed solutions are

Helical antennas, which are suitable for L-, S- and X-band applications

Toroidal antennas, which are suitable for S-, Ku- and Ka-band applications

Horns, which are suitable for Ku- and Ka-band applications

Waveguide radiators, which are suitable for C-, X-, Ku- and Ka-band applications, and

Patch-excited cups, which are suitable for L-, S- and X-band applications

Focusing on a few specific applications and frequency bands, it is first noted that helicesand patch-excited cups are the preferred solutions for GPS/GNSS applications. The latterantenna structure is also the main choice for S-band applications, since it can implementboth compact/low-gain and large/medium-gain antennas. At the X-band front, helices areused for high-speed data downlink. TTC antennas with hemispherical coverage come in two“flavours”: waveguide radiators for dual-frequency operation, and patch-excited cups forsingle-frequency operation.Patch-excited cups are truly versatile performers. They are light weight, robust, all-metalradiators, able to produce gains as high as 15 dBi. It can be roughly stated that theirradiation pattern is designed separately from their input matching. The pattern is mainlyinfluenced by cup diameter, rim height, and radius and height of the top-most patch. Inputmatching is mostly handled by adjusting the geometry of the cavity formed by the lowertwo patches and by changing the radial position of the feed probes. The cross-influenceamong these parameters is weak enough (Wettergren et al., 2009). The GPS cup describedin (Zackrisson, 2007) covers both L1 and L2 bands, achieving peak gains equal to 8.5 dBi and7.4 dBi, respectively. With a cup diameter of 160 mm, and given that rim height is abouta quarter-wavelength, it is estimated that the corresponding electrical sizes are (ka)L1 =2.82 rad and (ka)L2 = 2.20 rad. On the other hand, the S-band cup that was designed for


the LCROSS mission is a medium-gain antenna (MGA). It scored a peak gain of 12.5 dBi at2.2 GHz, combined with an 18.2% fractional bandwidth. Nonetheless, higher gains demandlarger apertures (Harrington, 1960; Skrivervik et al., 2001), thus it comes as no surprise that itselectrical size is estimated in the range 4.10 < ka < 4.35 rad.3 Lastly, two patch-excited cupswere implemented for X-band TTC applications, using different receive (RX) and transmit(TX) frequencies. The RX antenna achieves 8.9 dBi of gain, whereas the estimated electricalsize of the radiating parts is (ka)RX = 2.63 rad at 8 GHz; the choke ring has been excluded fromthis calculation. The TX antenna achieves 7.5 dBi of gain, whereas the estimated electrical sizeof the radiating parts is (ka)TX = 2.24 rad at 8 GHz; the mounting flange has been excludedfrom this calculation.

3.2.2 Work described by Gao et al., IEEE Antennas Propag. Mag., 2009The third and final contribution is by (Gao et al., 2009). The authors presented an excellentoverview of the status of antennas for small satellites until the end of 2007. Work from manygroups was included, albeit the focus was on the work done in this area by the University ofSurrey, Surrey Satellite Technology Ltd., and the Surrey Space Centre.The article takes off with an introduction to small satellites, describing their modular structureand the modules they have in common. Examples of several small satellite projects arethen given, including remote-sensing micro-satellites; a student-built multiple–pico-satellitesystem, with a “mother-ship”–“daughter-ship” arrangement, used for communications andas a scientific test-bed; multi-university student-built nano-satellites used for a variety ofpurposes; and pico-satellite systems being built and used by a wide-ranging internationalcollaboration (the CubeSat programme).The functions and commonly used types of antennas for such small satellite systems arediscussed, followed by a discussion of antenna design challenges. Due to the specialenvironment in space and the requirements of modern satellites, there should be carefulconsideration of electrical, mechanical and thermal performance constraints. Yet anothermajor consideration for antenna design is the interaction between antennas and modernsmall-satellite structures. The chassis of the spacecraft is a finite 3-D ground plane, whichcouples strongly to the radiating elements, causing electromagnetic scattering and radiationpattern blockage. These problems intensify the importance of electromagnetic simulationsand measurements in an effort to obtain antenna placement for optimum performance andcoverage.The article then presents a detailed examination of the antennas used for each of the majorfunctions associated with small satellites. Antennas for TTC applications include monopoles,PIFAs, patches, QHAs and patch-excited cups. The range of frequencies covers the VHF,UHF, S-, C- and X-bands. Antennas for high-speed payload data downlinking include S- andX-band QHAs; compact MGAs based on the SAP principle; X-band, mechanically-steered,high-gain horn antennas; deployable parabolic reflectors; S-band patch-excited cups; andUHF through S-band active antennas for CubeSat missions based on the grid oscillatorconcept. Antennas for satellite navigation and positioning include medium-gain patch arrays,patch-excited cups and ceramic-loaded QHAs. Inter-satellite cross links can be facilitated byhigh-gain patch arrays and deployable reflectors, however the most attractive option seemsto be the use of low-complexity, self-steering, retrodirective arrays. In each of these areas, therequirements for the antennas are explained, followed by many examples of antennas thathave been used to meet these requirements.

3 The ambiguity stems from the fact that the top-most patch stands much higher than the edge of the rim.


The conclusions of the article display that this research area is flourishing, while numerouschallenges remain wide open to further investigation. Innovative concepts such as“satellite-on-PCB” (PCB-Sat), where the whole satellite is built on a single PCB, as well as“satellite-on-chip” (Chip-Sat), where the satellite is built in a single chip, are paving theway for cooperative small-satellite networks with sophisticated functionalities. To satisfy therequirements of next-generation satellite communication systems, much more work is clearlypending at the antenna front.

3.3 Overview of techniques pertinent to the chapterOne of the techniques used in this Chapter is an extension of the method introduced by (Notiset al., 2004). The authors etched 40 equally long slits along the periphery of a square microstripantenna, thus producing a meandering (ragged) outline. The ten slits on each side of the patchcovered one-third of its length. (Notis et al., 2004) showed that the disturbance of the currentdistribution could easily bring about a 30% size reduction for a given frequency; this reductioncould even reach levels up to 44%. Alternatively, a reduction in operating frequency up to 25%can be obtained, given the size of the patch.In (Kakoyiannis & Constantinou, 2008), the authors extended this slit-loading technique bytapering the length of the slits, and thus modulating their length in the spatial domain. It wasbriefly shown therein that the manipulation of the spatial distribution of the slits can resultin greater reduction in size and is also a way to control the input impedance Zin(jω) of theantenna. This Chapter is a detailed record of that modified miniaturization technique, whichmodulates slit length in order to spread the slit distribution further along the periphery of thepatch.One of the earliest studies on the use of slits in microstrip antennas was presented by (Zhang& Yang, 1998), who studied the effect of transverse slots in patches, i.e., straight slots that areperpendicular to the SCD and parallel to the phase front of the current. The authors proposedan equivalent circuit that characterizes the electrical behaviour of the slot; it is a multi-portnetwork of inductances appearing in series with current flow. Experimental data displayed a23% reduction in resonant frequency. This reduction can climb up to 40% if the straight slot isreplaced by an “H”-shaped slot. Optimal slot positioning was also investigated: since the slotis inductive, it should be etched where the current is maximum, that is, at the very centrelineof the patch. On the other hand, the authors did not consider the effect of slot width, which,in our opinion, provides a significant extra degree of freedom to further increase the electricallength of the patch.A slightly more complex technique was presented in (Row et al., 2000), where four “Γ”-shapedslots are arranged in a cross order. By proper choice of slot length and inter-slot distances, a25% reduction in f0 can be achieved. Instead, the two wide longitudinal slits used by (Wong& Hsu, 2001) do not increase the electrical length of the patch; their placement does littleto alter the SCD. However, it was experimentally proven that they augment bandwidth. Thesame holds for the application of “U”-shaped slots; U-slotted antennas have been investigatedextensively in the open literature, and a complete design methodology is presented in(Weigand et al., 2003).Particularly useful are techniques that achieve simultaneous size reduction (an increase inelectrical length) and bandwidth enhancement. One such method unfolds in (Xiao et al.,2005), where an inset-fed patch antenna is loaded by asymmetric (alternate) peripheralslits. The slits were etched along the non-radiating edges of the patch, and achieved a 60%reduction in antenna size. At the same time, with a little help from the inset feed, two


different Transverse-Magnetic (TM) modes are excited: TM10 and TM01. These modes arefrequency-adjacent, and thus manage to double the Voltage Standing Wave Ratio (VSWR)bandwidth: these compact patch antennas displayed a fractional bandwidth close to 4%.The same research group capitalized once more on asymmetric slit loading in (Xiao et al.,2006). The new slit arrangement excites two frequency-adjacent TM10 modes, and managesto produce even better results in terms of size reduction and bandwidth augmentation.However, none of the above techniques is suitable for circularly polarized antennas, sincethey fail to preserve the required double symmetry. Therefore, in order to implement theCubeSat antenna, we decided to extend the technique presented in (Notis et al., 2004).

4. Hybrid Feed Network Design and Simulation Setup

4.1 A hybrid feed network for circular polarizationThe communications antenna is used by the orbiter in both transmit (Tx) and receive (Rx)modes. Therefore, it is essential that identical radiation characteristics are maintained betweenmodes. According to the Reciprocity Theorem (see §1.3 and §9.4 in (Stutzman & Thiele, 1998)),an antenna will maintain its properties as long as it is made out of bidirectional elements.This requirement holds not only for the body of the radiator, but for its feeding network aswell; no diodes or transistors are allowed in the circuit for reciprocity to hold exactly. On theother hand, a purely passive antenna-plus-feeding-network combination will be reciprocalby definition. The hybrid coupler presented in this Section is a purely passive, bidirectionalfour-port microwave circuit (Bahl & Bhartia, 2003; Gustrau & Manteuffel, 2006). The model ofthe coupler used in simulations is shown in Fig. 1, which also indicates port numbering; ports1 and 4 lie on the transceiver side, whereas ports 2 and 3 lie on the microstrip antenna side.

Fig. 1. Perspective view of the hybrid coupler model.

When in Rx mode, the coupler combines the signals arriving at ports 2 & 3 and produces asingle output at port 4. Port 1 is (ideally) completely decoupled from port 4, that is, in theory

we get S14Δ= 0 and no signal power appears at port 1. When in Tx mode, the output signal

coming from the High-Power Amplifier (HPA) drives port 1. This signal is divided into twosignals in phase-quadrature (Δφ = 90◦), with each signal carrying 3 dB less power than theinput signal. Thus, this circuit is essentially a power divider that introduces an excess phase


delay to one of the two branches. Port 4 is isolated from port 1, that is, theoretically S41Δ= 0

(Gustrau & Manteuffel, 2006).The hybrid coupler is very well documented in the literature pertaining to microwavesolid-state circuits (Bahl & Bhartia, 2003). As a result, initial predictions of the dimensionsof the transmission lines that make up the coupler are readily available from theory. Beforecalculating any estimated values, it is important to reach a decision regarding the microwavesubstrate on which the coupler will be printed. The coupler is essentially composed of fourλg/4-long microstrip lines. The designer must make sure that the guided wavelength λg

is short enough for the whole coupler to fit on a 100 × 100 mm2 area. After surveying thesubstrate market, the military/space-graded Rogers TMM 10i™ ceramic substrate was chosen(εr = 9.80, tan δe= 0.0020). Other substrates suitable for the coupler are Rogers RT/Duroid6010LM; Rogers TMM 10; Rogers RO3010; Rogers RO3210; and Arlon AD1000. The chosensubstrate height was H = 3.2 mm, and this is one of the advantages of TMM 10i. The thicknessof the copper cladding was assumed to be 35 μm (1 oz Cu).The design of a high-frequency circuit is an iterative procedure, even with today’s advancedfield solvers. The solvers decrease the number of iterations significantly, but a few iterationsare always required for first-pass success on the test bench. In this context, the initialsimulations revealed that the theoretical estimations for the dimensions of circuit elementsneeded some improvement. On the one hand, the coupler did not resonate at the desiredfrequency, whereas on the other hand, power was not divided equally between the twobranches. To improve the design further, a parametric study was undertaken, whichconverged quickly to the proper circuit dimensioning that satisfies coupler specifications. Theconverged values are shown in Fig. 2.

Fig. 2. Converged values of the lengths and widths of the microstrip lines of the hybridcoupler model. All dimensions are in millimetres.

4.2 Numerical resultsThe scattering (S-) parameters of the 90◦ hybrid are depicted in Fig. 3. The excitation wasapplied to port 1, which is properly matched to the 50-Ω system impedance: S11 < −40 dB.


Port 4 is strongly decoupled from port 1: S41 < −30 dB. Power impinging on port 1 is equallydivided between ports 2 and 3, since S21 ≈ S31 ≈ −3 dB. The corresponding phase diagrams(not shown here) indicate that the phase lead/lag between the signals at ports 2 & 3 is Δφ23 =90.1◦.Fig. 4 and Fig. 5 illustrate the amplitude and phase balance of the coupler, respectively. Theoperational bandwidth of this circuit can be defined in various ways, exactly like an antenna.So, let us choose four proper definitions:

1. The available bandwidth for a 2:1 VSWR, that is S11 < −10 dB, equals BWhybridV =

149 MHz or, stated in fractional terms, FBWhybridV = 34%.

2. Instead, the frequency range where the isolation between ports 1 & 4 is better than 20 dBis much narrower: BWhybrid

iso20dB = 46 MHz.

3. The operational bandwidth for a ±5◦ phase balance is BWhybrid±5◦ = 148 MHz.

4. The operational bandwidth for a ±1 dB amplitude balance is BWhybrid±1dB = 140 MHz.

Fig. 6 is an illustration of the surface current distribution on the conductive parts of thecoupler; the dielectrics have been made invisible to get a clear view of the currents. Currentamplitude is shown as concurrent maximum values at every point along the circuit. Of course,concurrent maxima are physically impossible because of phase shifting across the circuit; thisis just a graphical tool that helps the designer identify “hot” and “cold” areas. From this roughthermograph it is obvious that power entering the circuit at port 1 is equally divided betweenports 2 & 3, whereas almost no power exits from port 4.

Fig. 3. Magnitudes of the S-parameters of the converged hybrid model. These parameterswere obtained by exciting port 1 and terminating all other ports at the system impedance.

4.3 Field solver and generic simulation setupAll microwave systems were designed and simulated in a Transient Solver (TS) that is partof the CST Microwave Studio™ full-wave electromagnetic suite. The TS applies the FiniteIntegration Technique (FIT) in the time domain to reformulate Maxwell’s integral equations


Fig. 4. Amplitude balance variation (in dB) between ports 2 & 3. Amplitude imbalance lessthan ±1 dB is maintained for a 140-MHz bandwidth.

Fig. 5. Phase balance variation (in degrees) between ports 2 & 3. Phase imbalance less than±5◦ is maintained for a 148-MHz bandwidth.

Fig. 6. Concurrent maximum values of the surface current distributed along the coupler.Note the absence of current flowing out of port 4.

into the so-called “Maxwell Grid Equations” (Gustrau & Manteuffel, 2006; Munteanu et al.,2010; Vasylchenko et al., 2007a; Weiland et al., 2008). By applying Yee’s spatial discretization


scheme and Courant’s maximum stable time-step, FIT results in the same set of equations asthe Finite-Difference Time-Domain (FDTD) technique (Gustrau & Manteuffel, 2006). The TScalculates the broadband behaviour of electromagnetic (EM) devices in a single simulationrun, with an arbitrarily fine frequency resolution, thus without missing any resonance peaks(Vasylchenko et al., 2007a).Time-domain solvers are particularly suitable for designing wideband antennas and passivemicrowave systems such as waveguide components, filters, couplers and connectors. Foractive microwave design, co-simulation is required between the EM solver and a non-linearcircuit simulator, such as Agilent Advanced Design System™ or APLAC™. TSs like CSTMWS can easily handle exotic materials, such as frequency-dependent (dispersive) andferri/ferro-magnetic materials. The ability to naturally include such difficult materials inmodels is one of the main strengths of TSs over FEM- and MoM-based solvers, althoughthe two latter have recently improved their material-handling capabilities (Vasylchenko etal., 2007b).A spatially non-uniform (adaptive) hexahedral mesh discretized the objects and the solvablespace in between. The mesh was refined four-fold near the edges of Perfect Electric Conductor(PEC) objects and inside the substrate to capture the large gradients of the E-field. Tetrahedralmeshing is possible through Floquet modes only when FIT is applied in the frequency domain,in which case the technique results in the Finite Element Method (FEM). Nevertheless, the FITengine used here employs the Perfect Boundary Approximation (PBA) technique (Munteanuet al., 2010; Weiland et al., 2008), and therefore the hexahedral mesh did not result in any objectstaircasing whatsoever.A wideband Gaussian pulse excited the structures; its spectral content ranged from DC to0.8 GHz. The simulator stopped when the initial system energy decayed by 50 dB. Thiswas a good trade-off between simulation speed and truncation error in the FFT engine thattranslates the results from the time- to the frequency-domain. It is also a good trade-off forthe near-to-far-field transformation that produces the far-field pattern of an antenna out ofthe fields calculated in the near-field. The maximum cell size at the maximum frequencyfmax (smallest wavelength λmin) was set to a small fraction of λmin. The solvable space wasterminated at an adequate number of Bérenger Perfectly Matched Layers (PML) (Bérenger,1994), which had a normal (broadside) reflectivity of −80 dB. The distance of every objectfrom the boundary of the solvable space was set equal to λc/8 = 300/(8× 0.4) mm = 94 mm,unless otherwise noted.Whenever a model featured topological symmetry and satisfied the appropriate boundaryconditions for the electric/magnetic tangential components and the magnetic/electric flow,an electric/magnetic wall was placed across the plane of symmetry. This boundary conditionreduced the computational burden significantly without loss of accuracy, because only afraction of the structure needed solving. Complexity depends upon the level of detailexhibited by the objects comprising the model and the electrical size of the solvable space.All structures that were modelled as part of this Chapter were fully parametrised. Thekey concept here is that, if the objects in a model are defined with parameters insteadof numbers, then the designer benefits from parametric studies and optimization. Ina sense, parametrisation creates “inflatable” models—like an accordion—instead of fixed,“frozen” models. Parametric sweeping and optimization jobs can be distributed across many“worker” computers through the corporate LAN and run in parallel. This basic form oflaboratory/company distributed computing power exploitation brings about significant timesavings for the design team.


4.4 Solver settings applied to the hybrid couplerFig. 7 depicts the spatial discretization (better known as grid formation or meshing) of the modelused to design the 90◦ hybrid. The structure was excited in the time domain by a Gaussianpulse having spectral content in the range DC–0.8 GHz. The excitation signal along with thefour output signals are shown in Fig. 8.For efficient simulations, that is, simulations that strike a good balance between speedof execution and result accuracy, a spatially non-uniform (adaptive) grid was designed;maximum allowed grid step was equal to λg/50 at 0.8 GHz. No form of packagingwas adopted, thus the rectangular solvable space surrounding the PCB of the couplerwas terminated at a 4-layer Bérenger PML structure (Bérenger, 1994); these are open-spaceboundary conditions. This circuit is non-radiating, thus a 4-layer boundary absorber is morethan adequate. However, to increase the speed of iterations, the solvable space was trimmedto half by terminating the area below the substrate at a PEC condition, i.e., Et ≡ 0. Thisapproximation is valid because, when the coupler is studied in solitude, it is a non-radiatingsystem (at least intentionally). Therefore, it is safe to assume that the ground plane of thePCB extends to infinity—this is precisely the computational effect of the electric boundarycondition. The complexity of the model was 60 × 79 × 14 = 66, 360 Yee cells.

Fig. 7. The grid on which the electromagnetic problem was solved displayed a variable stepranging from 0.6 mm to 2.4 mm. Maximum grid step corresponds to λg/50 (or λ0/156) at themaximum frequency fmax = 0.8 GHz.

5. Inductive-slit-loaded Microstrip Antenna design

5.1 Antenna design considerationsExamples of microwave substrates suitable for the antenna are Rogers RT/Duroid™ 6006and Rogers RO3006™. Both present a dielectric strength εr = 6.15, and approximatelythe same loss tangent; the former displays tan δe= 0.0019, whereas tan δe= 0.0020 for thelatter. However, production heights differ: Duroid 6006 can be purchased laminated with amaximum height H6006

max = 2.54 mm= 100 mil, whereas RO3006 is sold at a maximum height


Fig. 8. Voltage signals, in the time domain, being input (“i1”) and output ( “ox,1”, wherex ∈ {1, 2, 3, 4}) from the ports of the hybrid coupler. System stored energy decayed to thepoint of terminating the execution after 10.5 ns of simulation time.

H3006max = 1.27 mm= 50 mil. In any case, the height chosen for the CubeSat antenna substrate

was equal toHpatch = 6.4 mm = 252 mil (1)

and thus bonding of several single-side-laminated substrates with prepregs is required.The initial design stages of the antenna started out on the assumption that the same dielectricmaterial used for the coupler would also be used for the patch antenna (Rogers TMM 10i™, εr= 9.80, H = 3.2 mm). On the TMM 10i the antenna resonated at 440 MHz for a square patchlength Lini = 108.3 mm. With a rough frequency scaling, it was estimated that the antennawould resonate at f0 = 436.5 MHz for a length L′

ini = 109.2 mm. After scaling the dielectricconstants, it was estimated that an antenna built on Duroid 6006 or RO3006 would have aresonant length

L′′ini = L′

ini

√9.806.15

= 137.8 mm. (2)

In theory, the resonant length of a microstrip patch antenna that corresponds to the consideredparameters equals

Ltheoryres = 0.49

λ0√εr

= 135.8 mm. (3)

The deviation between the results in (2) and (3) is a mere 1.5%.From the handy analysis unfolding in Chapter 5 of (Stutzman & Thiele, 1998) the followingestimation on the real part of the input impedance of the patch can be extracted,

RinΔ= ZA = 90

(ε2

rεr − 1

)( Lpatch

Wpatch

)2

. (4)

Substituting εr = 9.80 and Lpatch = Wpatch, we obtain

RinΔ= ZA = 90

(9.80)2

9.80 − 1Ω = 982 Ω. (5)


This uselessly high resistance is a side-effect of the high εr . This value can be reduced downto 50 Ω by setting

L′patch

W ′patch

=1

4.43. (6)

Because of the severe space constraints on the spacecraft, we cannot afford to design arectangular patch; the initial study indicated clearly that only a square patch can fit in theallocated area. All of the above, combined with the fact that the high εr threatens to eliminatethe minimal bandwidth of the patch antenna, led us to the choice of the lower εr = 6.15. Thus,the theoretical estimation for the input resistance of the antenna now becomes

Rin = 90(

ε2r

εr − 1

)( Lpatch

Wpatch

)2

= 90(6.15)2

6.15 − 1Ω = 661 Ω. (7)

By extending the microstrip feed line inside the patch by a proper length Δxi the inset feedtechnique is employed; the modified input resistance becomes (Stutzman & Thiele, 1998)

Rinset = Rincos2(

πΔxiL

). (8)

Solving for Δxi/L, which is the fractional insertion depth, we get

ΔxiL

=1π

cos−1

(√RinsetRin

). (9)

Substituting Rin = 661 Ω and Rinset = 50 Ω we obtain the following insertion depth

ΔxiL

=1π

cos−1

(√50661

)= 0.411. (10)

The result in (10) means that the inset feed has to penetrate half-way along the surface of thepatch; to avoid this, we used a quarter-wavelength transformer (λg/4–Xformer). By tradingoff transformer impedance for a mechanically robust copper trace width, we chose the widthWquarter = 1.0 mm, which gives a characteristic impedance Zquarter = 117.5 Ω. The lengthof the transformer equals Lquarter = 87.0 mm, whereas the resistance that can be matched to50 Ω is

Zx =Z2

quarter

50Ω = 276 Ω. (11)

Now the initial estimation for the depth of the inset feed can be derived,

(ΔxiL

)quarter

=1π

cos−1

(√50

276

)= 0.360. (12)

However, this effort did not produce any significant reduction in inset depth; the reason is theslope of the curve shown in Fig. 9.The 2:1 VSWR bandwidth is approximately estimated by equation (13) for H � λ0 (Stutzman& Thiele, 1998)

FBWV = 3.77(

εr − 1ε2

r

)(Wpatch

Lpatch

)(Hλ0

). (13)


Fig. 9. Variation in required fractional inset depth as a function of the impedance seen at theedge of the patch.

Applying (13) for the parameters of this design gives the following fractional VSWRbandwidth,

FBWV = 3.77

[6.15 − 1

(6.15)2

](6.4

687.3

)= 0.0048. (14)

The value corresponds to just 2.1 MHz of BW at the center frequency f0 = 436.5 MHz. Thus, itis expected that the total application bandwidth BW = 3.2 MHz will be covered with a VSWRvalue higher than 2:1.

5.2 Antenna geometry evolutionThe number and arrangement of the peripheral slits along the edges of the CubeSat patchantenna have been influenced by the design strategy of (Notis et al., 2004). The authors usedslits of maximum length equalling 380 mil (9.5 mm) for a patch length 1620 mil (40.5 mm);slit depth was 23% of patch length. The slits were 20-mil (0.5-mm) wide, whereas inter-slitdistance was 40 mil (1 mm). The starting centre frequency of that study was f Notis

0 = 2.36 GHz.The frequency ratio between the two studies equals 5.4, therefore frequency scaling leads toroughly 2.5-mm wide slits with inter-slit spacing equal to 5.0 mm. The total edge lengthoccupied by the 10 slits in (Notis et al., 2004) was

W10total = 10 · 20 + 40 (10 − 1) mil = 560 mil. (15)

Consequently, the portion of the patch edge occupied by the slits is

5601620

=2881

13

,

which is a reasonable design choice, since provisions for circular polarization were made in(Notis et al., 2004) as well.The CubeSat antenna was designed by etching 10 slits on each of the 4 sides of the squarepatch. The slits have variable width (but equal for all), and also variable length that followsa certain set of values {a1, a2, a3, a4, a5}. To preserve the potential for circular polarization,


slit configuration has been chosen in a way that maintains the two perpendicular symmetryaxes (see Fig. 10). This is the reason why there are only 5 length variables in the previous set,instead of 10.Since the slits have been etched on the periphery of the patch and not, for example, on theground plane, the most natural way of spatially modulating (tapering) their lengths is thetriangular distribution. Theoretically, this tapering would force the current to go through thecenter of the patch, and thus produce an effective physical length

Leff = Lpatch√

2. (16)

Simulations of antenna models using the triangular tapering started out with a 33% total edgecoverage. The parametric sweeps indicated that the estimation of (12) was quite correct: theoptimal fractional inset depth lies between 0.36 and 0.38. It is obvious from Fig. 10 that theshape of the slits enables us to increase their width, and therefore occupy a larger part oneach side of the square; this leads to a greater miniaturization degree. The study indicatedthat good results are obtained when the slits take over 70–80% of every side. Furthermore, itwas discovered that a good compromise between miniaturization and bandwidth is obtainedwhen the ratio of slit width to slit gap is set around unity. Simulations showed beyond anydoubt that this ratio affects both f0 and Zin(jω). Changes in input impedance are critical andmust occur in a controlled manner: the CubeSat antenna is electrically small, thus it is ratherchallenging to tune it (Xin (jω) = 0) and match it (Rin (jω) � 50 Ω).Fig. 10 illustrates in perspective the final antenna geometry; the tall substrate is evident. Thisparticular model, which is just a 2-layer PCB, represents the first completed design stage; itis designated as the CubeSat Patch Prototype version 1 and abbreviated herein as “CSPP–1”. InSection 5.5 and Section 5.6 we will present the second completed design stage, abbreviatedherein as “CSPP–2”.The 40 transverse slits along the periphery of the patch increase the distance that currentmust travel to reach the opposite edge, and thus increase the effective electrical length of theradiator. The increased electrical path, in turn, reduces the physical size of the patch below100 mm. If the antenna were designed on a foam substrate (εr 1.0), then the nominal patchsize would be 344× 344 mm2. This nominal area was initially reduced by 84% due to dielectricloading; the area of the resulting patch was further reduced by 55% due to the slit distribution.Patch side length was reduced by 60% and 33%, respectively. The final antenna converged todimensions 93 × 93 mm2. Its area was reduced 13.7 times; side length was reduced 3.7 times.Fig. 11 depicts all important dimensions of both the microstrip patch and the substrate. Thesize of the substrate has been increased beyond 100 × 100 mm2 to facilitate the incorporationof the feed network in the same model (i.e., the λg

4 transformer and a small segment of 50-Ωmicrostrip).The length of the slits was modulated according to the triangular distribution. Otherdistributions can also be used, such as binomial, uniform, geometric and cosine-on-pedestal.In fact, (Notis et al., 2004) used the uniform distribution. A first estimation on the electrical

size of the radiator is ka = 2π93√

2/

2687.3 rad = 0.60 rad < 1 rad, and thus the CubeSat antenna

is indeed electrically small. It remains to be seen how well can such a small cavity-like antennaperform in terms of gain, radiation efficiency, quality factor, bandwidth and half-power beamwidth.

5.3 CSPP–1 simulation setupFig. 12 depicts the spatial discretization (meshing) of the model used to design the CSPP–1antenna. The structure was excited in the time domain by a Gaussian pulse having spectral


Fig. 10. The square printed CSPP–1 antenna loaded with inductive peripheral slits. The λg/4transformer and a small segment of 50-Ω microstrip line are also shown.

Fig. 11. Converged dimensions of the final model, as they resulted from the optimizationprocess. The circuit is printed on a Rogers RO3006 substrate (εr = 9.80, tan δe= 0.0020,H = 6.4 mm). All dimensions are in millimetres.

content in the range DC–0.8 GHz. For efficient simulations, a spatially non-uniform (adaptive)grid was designed; maximum allowed grid step was equal to λg/36 at fmax = 0.8 GHz. Therectangular solvable space surrounding the PCB of the antenna was terminated at a 6-layerBérenger PML structure (Bérenger, 1994); an antenna cannot be properly simulated unless itis terminated at open-space (“radiating”) boundary conditions. Based on our prior experiencewith the T-Solver, the 6-layer PML provides an excellent accuracy/speed trade-off, in thesense that antenna radiation characteristics converge while simulation time does not increasenoticeably (Kakoyiannis et al., 2010; Kakoyiannis & Constantinou, 2010a;b).Setting the Boundary Conditions (BCs) properly in an antenna simulation is always a majorissue. During the CSPP–1 design stages, where high simulation speed was preferred overextreme accuracy, the solvable space was trimmed to half by terminating the area below thesubstrate at a PEC boundary condition, i.e., Et ≡ 0. This causes the ground plane of the PCB


Fig. 12. The grid on which the electromagnetic problem was solved displayed a variable stepranging from 0.3 mm to 4.2 mm. Maximum grid step corresponds to λg/36 (or λ0/90) at themaximum frequency fmax = 0.8 GHz.

to extend to infinity; now, the mirror backing the patch becomes electrically huge. This is onlya practical approximation, since in reality the patch occupies approximately the same area asthe ground plane does.Yet another important BC-related issue is raised by the geometry of the antenna, i.e., the twoperpendicular symmetry planes: could electric/magnetic BCs be applied to the model so asto reduce the solvable space to a fraction ( 1

2 , 14 , 1

8 ) of the original? Indeed, after studyingthe volume field distributions inside the solvable space, one can notice right away that at theboundary of xz-plane the magnetic field H(x, y, z, t) is normal to the plane (Ht ≡ 0), whereasthe electric field E(x, y, z, t) is tangential. This means that through the xz-plane there is onlymagnetic flux, and no electric. Therefore, at the xz-plane a magnetic BC (or magnetic wall) isapplicable; this BC reduces the computational burden to one-half without any loss of accuracy.Fig. 13 illustrates the application of the magnetic wall. Magnetic symmetry was maintainedthroughout the design stages of the CubeSat antenna. The complexity of the CSPP–1 modelwas 127 × 57 × 39 = 282, 321 cells.

5.4 Numerical electrical performance of the CSPP–1 antennaAfter the geometry of the antenna was established, the next (and most important) steptowards design closure was to resonate the antenna. Tuning (Xin (jω0) ≈ 0 Ω) andmatching to 50 Ω (Rin (jω0) ≈ 50 Ω) must be accomplished at the desired frequency withoutviolating any of the other specifications. The result of this procedure is documented throughS-parameters and the Smith chart in Fig. 14 and Fig. 15 respectively. The matching/resonancedepth is satisfactory (|S11| ≈ −18 dB), albeit resulting in a narrowband antenna, as expected.It achieves a 2:1 VSWR bandwidth BW−10dB = 2 MHz, and a 3:1 VSWR bandwidth equal toBW−6dB = 4 MHz.The Smith chart shows that the antenna behaves like a capacitor or inductor for most of thefrequencies. This is an anticipated result; the antenna is electrically small (this is proven inSection 5.6). Inside its operational bandwidth, a single resonance exists (dXin/dω > 0). Theswift crossing of the curve through the central area of the chart recounts the small achievablebandwidth.According to the cavity model, which provides an adequate theoretical treatment of microstripantennas, the dominant component of the electric field is Ez = Eziz. Fig. 16 illustrates the


Fig. 13. By applying the magnetic BC Ht ≡ 0 across the xz-plane (blue frame), we get tosimulate only the left half of the solvable space, while obtaining equally accurate results. Thecombination of the magnetic symmetry with the electric BC below the substrate havereduced the computational burden to 1/4.

Fig. 14. Resonance and matching at the input of the CSPP–1 antenna given by the magnitudeof the input reflection coefficient.

magnitude of the total electric field E(x, y, z) = Exix + Eyiy + Eziz taken at a snapshot whenthe field is maximum. Notice that the electric field is strongest not only at the two radiatingedges, but also along other vertices along the patch; this is due to the presence of the 40 slits.However, as is well-known from theory, the broadside radiation of microstrip antennas doesnot result from the z-component of the E-field, but from the two tangential componentsproducing the fringing field at the radiating edges of the patch. Fig. 17 illustrates a snapshot ofthe peak magnitude of the tangential electric field Et = Ex +Ey. Notice how the high-εr keepsthe fringing fields too close to the patch. This an ominous conjecture in terms of radiationefficiency; the antenna will tend to behave as a resonant cavity with a small radiating leakage.


Fig. 15. The CSPP–1 antenna resonates near f0 = 436.5 MHz showing an input resistanceRin ≈ 40 Ω.

Fig. 16. Maximum magnitude of total E-field in the vicinity of the patch. The colour code wasset to a logarithmic scale for better resolution.

During all design stages it was very important to check whether the slit distribution wouldforce antenna miniaturization. Visualization of the surface distribution of the current is theway to go; this extremely useful design tool is illustrated by the vector field in Fig. 18. It isevident that the slits do not allow current to travel on a straight line from one radiating edgeto the other. Rather, the current moves on a broken line, crossing the center of the patch. Thus,the electrical length of the antenna indeed increases by a factor dependent on maximum slitlength.The study of the CSPP–1 antenna is concluded with the presentation of numerical resultspertaining to far-field radiation characteristics. Fig. 19 depicts the three-dimensional (3-D)far-field pattern of the antenna embedded into the model. This pattern was calculated atf = 437 MHz and its key aspects are low gain and average radiation efficiency, as it was


Fig. 17. Surface distribution of the peak magnitude of the tangential E-field around the patch.The colour code was set to a logarithmic scale for better resolution.

Fig. 18. Visualization of the current distribution on the CSPP–1 patch as a vector field. Thecolor code has been set to logarithmic scale for greater detail.

already predicted:Gmax = −1.2 dBi

nrad = 0.53 = −2.8 dB

}(17)

As a direct consequence of the results in (17), the input resistance of the CSPP–1 antenna

Rin (jω)Δ= � {Zin (jω)} is comprised at resonance by the following two parts:

Rrad = 21.2 ΩRloss = 18.8 Ω

}(18)

The shape of the far-field pattern is anticipated from theory. The abrupt cut is due tothe electric boundary condition applied below the substrate; this BC prohibits radiationin the lower semi-space. Therefore, at this design stage there is no information availableon the back-lobe. Significant backward radiation is anticipated because of the comparabledimensions of the patch and the ground plane.A CubeSat is intended to communicate with its ground control within a given frequencyrange, which the antenna designer must match to the operating bandwidth of the antenna.


Fig. 19. The gain values of CSPP–1 remain below 0 dBi for all directions in the uppersemi-space owing to low radiation efficiency. Radical changes are expected in the morerealistic CSPP–2, where the back-lobe will enter the visible region of the pattern.

It would be very useful for the satellite link designer to have information on antenna gain notjust for one frequency, but for the whole range of frequencies. To this end, broadband far-fieldmonitoring and recording was facilitated by 17 field monitors uniformly spaced across the3.2-MHz bandwidth. This recording provided the broadband variation in radiation efficiencynrad (see Fig. 20), total efficiency ntotal (see Fig. 21) and gain (see Fig. 22).

Fig. 20. Broadband variation in the radiation efficiency of the CSPP–1 antenna.

5.5 CSPP–2 simulation setupThe CSPP–2 antenna is a far more realistic model compared to CSPP–1. Two importantchanges were made to this second prototype: first, the electric boundary condition belowthe substrate was removed. Thus, all 6 BCs were set to open-space (radiating). The solvablespace was terminated at a 6-layer PML, which was separated from every side of the modelby λc/8 at fc = 0.4 GHz. Second, a solid PEC rectangular object was mounted right belowthe substrate, pressing against the ground plane. This PEC object is 100 mm tall, whereasits transverse dimensions are equal to those of the ground plane. It models the chassis ofthe satellite; it is useful for studying the behaviour of the antenna in what looks like its trueoperating environment. The realistic CSPP–2 model is depicted in Fig. 23.


Fig. 21. Broadband variation in the total efficiency of the CSPP–1 antenna.

Fig. 22. Broadband variation in the IEEE gain of the CSPP–1 antenna. Peak-to-peak gainflatness equals 0.3 dB.

This was the most complex model that was solved in the framework of this Chapter; thecomplexity of the solvable space was 143 × 68 × 44 = 427, 856 hexahedral cells. Note thatthe magnetic symmetry across the xz-plane is still applicable. Fig. 24 shows the full solvablespace annotated by the 6 boundary conditions.

5.6 Numerical electrical performance of the CSPP–2 antennaWith the planar antenna mounted on the PEC chassis, the first thing that was noticed aboutits behaviour was that the resonant frequency remained almost constant; it shifted slightlydownwards from f0 = 436.5 MHz to f ′0 = 436.0 MHz. However, there was a significantchange in input resistance, which dropped from Rin (jω0) = 40 Ω to R′

in (jω′0) = 23 Ω. The

drop can be compensated by reducing the depth of the inset feed, but this is hardly the issuehere: this 42% reduction epitomizes the fact that antenna design iterations end only after theantenna has been embedded into its working environment, be it a satellite, a cell-phone heldby a hand next to a head, a vessel at sea, and so on. If the working environment is not takeninto account, even as a very crude model, the system designer will have to settle for an antennaof sub-optimal performance.The shape of the |S11| curve is essentially preserved, but minimum reflection coefficientincreases from −18 dB to −9 dB. The operational bandwidth for a 3:1 VSWR (S11 ≤ −6 dB)remains at BW−6dB = 4 MHz. Fig. 25 illustrates the variation in Zin(jω) on the Smith chart.


Fig. 23. A 100-mm tall conductive chassis was embedded into the realistic model. The othertwo sides are longer to fit the size of the substrate. All dimensions are in millimetres.

Fig. 24. By applying the magnetic BC Ht ≡ 0 across the xz-plane (blue frame), we get tosimulate only the left half of the solvable space, while obtaining equally accurate results. Thistime, however, there was no electric BC below the substrate.

The far-field pattern of the CSPP–2 model is certainly more intriguing than thetextbook-looking one of CSPP–1. The 3-D pattern shown in Fig. 26 confirms the existenceof a strong back-lobe, which is created by near-field diffraction on the edges of the groundplane and the PEC chassis. Maximum directivity is Dmax = 4.9 dBi, but the low efficiencyresults in a maximum gain Gmax = 0.7 dBi at f ′0 = 436 MHz.The pattern cuts at the principal planes φ = 0◦ and φ = 90◦ are illustrated in Fig. 27. Theytoo indicate that there is a strong back lobe caused by the patch and the ground plane having


Fig. 25. The CSPP–2 antenna resonates at 436 MHz showing an input resistance Rin ≈ 23 Ω.

Fig. 26. The 3-D far-field pattern of the CSPP–2 antenna drawn in spherical coordinates. Thedirection of main-lobe maximum deviates from broadside by 15◦ because of the inset feed,which shifted the phase center by 30 mm along the central axis of the patch.

comparable dimensions. The Front-to-Back Ratio (FBR) of the antenna is FBR = 5 dB, whereasits beamwidth is HPBW = 116◦ at both principal planes. After examining the three pattersas a whole, one could suggest that the far-field pattern of this electrically small antennaapproximates the isotropic radiator within 5 dB.Broadband far-field monitoring and recording was also performed for the CSPP–2 model.Recordings of the broadband variation in radiation efficiency nrad, total efficiency ntotal andgain are depicted in Fig. 28, Fig. 29 and Fig. 30 respectively.This section is concluded with the calculation of the electrical sizes of the two antennas. Theelectrical size is required for the calculations tabulated in Table 1. The vector SCD in Fig. 31indicates that the slit distribution works equally well for the CSPP–2 antenna. Therefore, thefollowing calculations apply to both antenna models.


(a) φ = 0◦ (b) φ = 90◦

Fig. 27. Pattern cuts at the φ = 0◦ and φ = 90◦ principal planes. On the latter plane thefront-to-back ratio is 0.5 dB higher (FBR = 5.3 dB).

Fig. 28. The radiation efficiency of the CSPP–2 antenna varies between 38–45% throughoutthe service band of the CubeSat.

First of all, we need to calculate the radius of the circumscribing sphere, that is, the thoughtspherical surface that circumscribes all radiating parts of the antenna. To this end, we have usedthe surface current distribution shown in Fig. 32. According to Sten’s theoretical treatment,the radius of the circumscribing sphere should be calculated by placing the centre at the feedpoint of the planar antenna (Bancroft, 2004; Sten et al., 2001). This holds for printed monopoleantennas, which, according to Image Theory, use a parallel ground plane to “mirror” the otherhalf of the antenna that is missing, thus becoming asymmetric dipoles. Obviously, microstrippatch antennas do not form an image, since they are nominally half-wavelength antennas.Therefore, the centre of the sphere was placed at the centre of the square patch. Apart from allthe above, the radius must be wide enough to accommodate the whole of the surface currentdistribution, i.e., the radiating parts of the antenna. Including just the patch may not suffice;currents exist also on the upper face of the ground plane below, and these currents contributeto radiation, too. This SCD is free to extend beyond the limits of the patch (Bancroft, 2004).This phenomenon occurs in CSPP–1 and CSPP–2: the lower SCD extends to the edges of


Fig. 29. The total efficiency of the CSPP–2 antenna varies between 29–33% throughout theservice band of the CubeSat.

Fig. 30. The maximum gain of the CSPP–2 antenna varies between 0.7–1.4 dB throughout theservice band of the CubeSat.

the ground plane. Finally, the radius of the circumscribing sphere is a = 64.2 mm, and theresulting electrical size of the antenna is

(ka)CubeSat = 2π64.2

687.3rad = 0.587 rad < 1 rad. (19)

Therefore, the radiator proposed in this Chapter is indeed an Electrically Small Antenna (ESA)(Hansen, 1981).

6. Discussing the results

Table 1 summarizes the electrical performance of the CubeSat antenna. Based on the tabulateddata, it is easy to derive the Quality Factor of the antenna from the relation (Yaghjian & Best,2005)

Q =

(2B

)·(

S − 12√

S

)(20)


Fig. 31. Visualization of the current distribution on the CSPP–2 patch as a vector field. Thecolor code has been set to logarithmic scale for greater detail.

Fig. 32. Definition of the radius of the circumscribing sphere for the CubeSat antenna.

where B is the fractional VSWR bandwidth and S is the corresponding VSWR. Setting S = 3,we get B = 0.0092, and (20) leads to a loaded Quality Factor

QCube =1

0.0092· 3 − 1√

3= 125.5. (21)

Another useful expression for calculating the loaded Q of antennas comes from (Pues & Vande Capelle, 1989)

QST =1B

√(TS − 1)(S − T)

S(22)

where T is the VSWR level that corresponds to the minimum reflection coefficient. In ourcase, min {|Γin (jω)|} = −18 dB, so the corresponding standing-wave ratio is S = 1.29.Substituting these values in (22) we obtain

QCubeST =

10.0092

√(1.29 × 3 − 1)(3 − 1.29)

3= 139 (23)

which is 10% higher than the estimation of loaded Q in (21).


Antenna Attribute ValueCentre frequency, f0 436.5 MHzSquare patch size, Lpatch 93.3 mm3:1 VSWR bandwidth, BW−6dB 4 MHzFractional VSWR bandwidth, FBWV 0.92%Electrical size, ka 0.587 radQuality factor, Q 125.5Lower bound on Q, Q�b 2.53Radiation efficiency at mid-band, nrad 38%Maximum gain at mid-band, GCube

max 0.7 dBi

Table 1. Overview of the electrical performance of the proposed antenna

The lower bound on Q according to Chu and McLean is calculated by the following equationafter substituting the values nrad = 0.38 and ka = 0.587 rad (Lopez, 2006; Skrivervik et al.,2001; Yaghjian & Best, 2005)

QCube�b = nrad

[(1ka

)3+

1ka

]= 2.53. (24)

It has been shown that, as a rule-of-thumb, it is safe to assume that a feasible antenna canachieve a quality factor 75% higher than the lower bound Q�b (Lopez, 2006). Assuming thatthe antenna maintains a constant radiation efficiency and electrical size, then the bandwidthcorresponding to a 75% higher Q is equal to

BWmax−6dB = 113.5 MHz (25)

or equivalently,BWmax

−10dB = 56.8 MHz. (26)

From the above we gather that a generic antenna of electrical size ka = 0.587 rad could achieve28 times as much bandwidth as the cavity-like CubeSat patch antenna with its inherentlynarrow bandwidth.Similarly, the upper bound on gain for an antenna of given electrical size ka that also achievessome meaningful operational BW is given by Harrington’s equation (Harrington, 1960;Skrivervik et al., 2001)

GCubeub = 10 log

[(ka)2 + 2 (ka)

]= 2.3 dBi. (27)

The upper bound on gain was approached by the CubeSat antenna within a margin

GCubeub − GCube

max = 1.6 dB (28)

which is very satisfactory. However, in the conclusions of his seminal paper, Harrington notesthat none of the concepts described therein holds for small antennas; thus the calculation in(27) is not valid, the reason being that small antennas are actually capable of significantlyhigher gains than the values predicted by the upper bound. But, Harrington’s equation canbe useful in the ESA case if we mirror the question: given the gain of the small antenna, whatwould its electrical size be if it were electrically large? This introduces the notion of effectiveelectrical size, (ka)eff. In our case, the effective size turns out to be (ka)eff = 0.48 rad, that is,


even smaller than the actual electrical size of the CubeSat antenna due to the low radiationefficiency. As a further example, let us assume that radiation efficiency could climb to 100%.This would produce a new gain value GCube

peak = 4.9 dBi, and the effective size would thenbecome (ka)eff = 1.02 rad.

6.1 Comparison with existing studiesThe first goal of a comparison is to be meaningful; only then will it produce some usefulconclusions. The literature review in Section 3 surveyed over fourty different antennatopologies, which spanned four different functions (see Section 2) and six different frequencybands. The statistics of the examined set reveal that 7% of antennas operated in the VHF band;29% operated in the UHF band; 10% operated in the L-band; 37% operated in the S-band;2% operated in the C-band; and 15% operated in the X-band. Different frequencies do notpose a problem: fractional bandwidth and electrical size are frequency–normalized quantities,whereas gain is related to directivity, which is determined by the electrical aperture. Hence, aninter-band comparison is still valid. Radiation efficiency is weakly dependent on frequency,so this attribute could also be included in the comparison. However, only (He & Arichandran,2001) have included details on nrad in their report.Different functions, on the other hand, can certainly be a problem. GPS/GNSS andTTC subsystems rely on low-gain, broad-beam antennas. Data downlinking and satellitecross-linking is done through medium-/high-gain, directive antenna systems. Increased gainrequires a large electrical size, period.4 Therefore, the electrical performance of the electricallysmall TTC antenna described herein is compared with the performance of previously reportedantennas aimed at GPS/GNSS and TTC subsystems. The comparison is shown in Table 2.5

The upper part of the Table is reserved for non-planar structures, whereas the lower parttabulates planar ones.Commenting on the tabulated results, it is first noted that quadrifilar helices (Niow et al.,2009; Rezaei, 2004) are wideband MGAs with clean circular polarization but they are alsoelectrically large structures (ka > 2 rad). With proper structure modification and extensivedielectric loading they can be shrunk down to resonant size, that is, the electrical size of thehalf-wavelength monopole. Bent-wire monopoles (Yousuf et al., 2008) are wideband antennaswith reasonable size. Their main drawback is that their performance degrades when mountedon a small satellite.Turning to the planar antenna regime, the antennas presented by (Mathur et al., 2001) aredirectly comparable with the CSPP antennas, particularly the UHF antenna. These areelectrically small, narrowband antennas as well. Their size exceeds that of the CSPP by 21%and 14% in the UHF and S-band case, respectively. At the other end of the design spectrum,the work by (Muchalski et al., 2004) is a typical example of how suspended, electrically largepatches can exhibit quite significant bandwidths. Furthermore, resonant-size patches canproduce gains in the range 4–6.5 dBi and bandwidths of a few percent (Gao et al., 2008;Hamrouni et al., 2009; Maqsood et al., 2010). On the other hand, 3-D structures consistingof folded and stacked radiating parts offer moderate bandwidths and gains combined, andcan even become electrically small (Lee & Woo, 2008). And last but not least, patch-excitedcups are electrically large MGAs offering significant gain values with respect to their size(Zackrisson, 2007). However, in their current form, their size is prohibitive for UHF CubeSat

4 Only compound field antennas threaten to alter this otherwise fundamental relationship, however thattopic is outside the scope of and space available in this Chapter.

5 The FBW cited for (Gao et al., 2008) is aggregate, not instantaneous.


Antenna Configuration f0 (GHz) FBW (%) Gmax (dBi) ka (rad)(Rezaei, 2004) 2.260 5.4 n/a 2.11(Yousuf et al., 2008) I 0.370 37.8 n/a 1.41(Yousuf et al., 2008) II 0.180 32.8 n/a 1.26(Yousuf et al., 2008) III 0.150 41.8 n/a 1.26(Niow et al., 2009) initial 2.600 30.8 4.0 2.22(Niow et al., 2009) Teflon 2.600 15.4 4.0 1.78(Niow et al., 2009) Macor 2.600 15.4 3.7 1.72(Mathur et al., 2001) UHF 0.450 1.6 n/a 0.71(Mathur et al., 2001) S-band 2.260 0.8 4.9 0.67(Muchalski et al., 2004) centre 2.450 8.2 n/a 2.24(Muchalski et al., 2004) edge 2.350 8.5 n/a 2.15(Muchalski et al., 2004) corner 2.275 7.9 n/a 2.08(Zackrisson, 2007) GPS L2 1.227 n/a 7.4 2.20(Zackrisson, 2007) GPS L1 1.575 n/a 8.5 2.82(Zackrisson, 2007) X-band RX 8.000 n/a 8.9 2.63(Zackrisson, 2007) X-band TX 8.000 n/a 7.5 2.24(Gao et al., 2008) 2.250 22.2 6.5 1.99(Lee & Woo, 2008) TX 2.487 6.6 5.3 1.39(Lee & Woo, 2008) RX 1.610 4.8 2.4 0.90(Hamrouni et al., 2009) 1 2.400 2.9 n/a 1.62(Hamrouni et al., 2009) 2 2.400 3.6 n/a 1.62(Maqsood et al., 2010) L1 1.575 1.0 6.3 1.82(Maqsood et al., 2010) L2 1.227 0.3 4.0 1.42This work, CSPP–2 0.437 0.5 0.7 0.59

Table 2. Comparison of electrical performance among GPS/GNSS/TTC antennas

missions since it is 3.7–4.8 times larger than the size of the CSPP, which fits marginally on thewall of the spacecraft.Judging by the sizes listed in the right-most column of Table 2, it becomes immediately clearthat antenna miniaturization techniques are utterly relevant to modern small satellites.

7. Conclusions and further research

Modern small satellites are designed and developed at costs and timescales that arerevolutionizing the satellite industry. These satellites range in size from 10–100 kg down toless than 100 g, take a year or less to develop and launch, and have individual costs rangingfrom a few million dollars to under $1,000. They achieve sophisticated functionality byutilizing state-of-the-art commercial off-the-shelf components, which are initially developedfor terrestrial applications and later adapted to space applications. Advances in low-powermicroelectronics and digital signal processing are turning satellites smaller, smarter, fasterand cheaper (Gao et al., 2009). The history and framework of small satellites were describedin Section 1. Within this framework, Section 2 defined the objectives of this Chapter. Section 3presented an overview of the status of antennas for such small satellites. Work from manyresearch groups around the world has been included. Although the focus was on planarantenna structures, linear and 3-D antennas were also described.


From the analysis, design procedure and results presented in sections 4, 5 and 6, it is clearthat designing a 1U CubeSat antenna at the lower end of the UHF spectrum is a challengingtask. There are too many constraints, and the designer cannot enhance one aspect of theantenna without seriously compromising another. The specifications lead inevitably to theimplementation of an electrically small antenna. The antenna must be made so small thatits performance suffers in every aspect. From the designer’s point-of-view, the feasibilityof implementing an electrically large antenna (ka > 2 rad), or even a resonant-size antenna(1 < ka < 2 rad), would be highly desirable. Such a radiator would have significantly betterperformance, and it would aid the link budget with its higher gain. The need for higher gainbecomes evident if we consider that the path loss for a CubeSat is about 140 dB.However, since the outer dimensions of CubeSats are fixed, there is really no point insuggesting modifications; the system would fall outside protocol specifications. The designercould suggest using more than one faces of the cube. This scenario also comes to no avail,since there can be only one Earth Facing Facet. Therefore, it seems that the only way to get abetter antenna would be to switch to higher frequencies and, more specifically, at least doublethe frequency (0.9 GHz). The higher frequency offers many design advantages and one veryimportant drawback: path loss increases by 6 dB. Will the new antenna system be able tocompensate this loss, so that it becomes worthy of the time required for the re-design?The answer is that there is indeed potential to cover the extra loss. Starting with 40 × 40 mm2

square patches over a 100 × 100 mm2 ground plane, we get the choice of increasing the patchwidth and switch to rectangular patches, which show better input matching, higher totalefficiency and broader bandwidth. Moreover, two rectangular patches forming a two-elementlinear broadside array can be fed in-phase with a corporate feeding network. Nonetheless,even if the orthogonal patches maintain the double orthogonal symmetry, axial ratio will shiftfrom unity and the purity of circular polarization will degrade.Another interesting topic for further research is to study different length distributions(tapering) for the peripheral slits. The triangular tapering seemed like a natural choice,but there are other options, e.g. binomial, cosine-on-pedestal, etc. It would be interestingto investigate how the other distributions perform in terms of the size-bandwidth trade-off,because each distribution will affect Leff and Zin(jω) differently.Finally, regardless of the frequency of operation of the CubeSat antenna, there is great interestin studying applicable techniques for broadband microstrip antennas. One such technique isthe etching of slots on the surface of the patch that are shaped after the letters “U” and “E”.This technique is presented in the most elegant way by (Weigand et al., 2003) and (Shafai,2007). Again, such broadbanding techniques destroy the double orthogonal symmetry of thepatch, and hence do not provide for clean circular polarization.

8. Acknowledgements

C. Kakoyiannis thanks Ms Calliope Raptis for proofreading and improving the manuscript,and Dr.-Ing. Dimitris Komnakos for the fruitful discussions on structure and content. Theassistance of both colleagues is gratefully acknowledged.The authors contribute this Chapter in loving memory of their colleague Dimitris T. Notis.Dimitris was a bright PhD student with the Department of Electrical Engineering, AristotleUniversity of Thessalonike, Greece. His sudden and untimely passing caused us great grief.


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